Bulletin of the Belgian Mathematical Society - Simon Stevin

On nuclearity of the algebra of adjointable operators

Massoud Amini and Mohammad B. Asadi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study nuclearity of the $C^*$-algebra $\mathbb B(\mathcal E)$ of adjointable operators on a full Hilbert $C^*$-module $\mathcal E$ over a $C^*$-algebra $\mathcal A$. When $\mathcal A$ is a von Neumann algebra and $\mathcal E$ is full and self dual, we show that $\mathbb B(\mathcal E)$ is nuclear if and only if $\mathcal A$ is nuclear and $\mathcal E$ is finitely generated. In particular, when $\mathcal A$ is a factor, then nuclearity of $\mathbb B(\mathcal E)$ implies that $\mathcal E$, $\mathcal A$ and $\mathbb B(\mathcal E)$ are finite dimensional.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 3 (2015), 423-427.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1442364589

Digital Object Identifier
doi:10.36045/bbms/1442364589

Mathematical Reviews number (MathSciNet)
MR3396993

Zentralblatt MATH identifier
1334.46042

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 18D05: Double categories, 2-categories, bicategories and generalizations

Keywords
Hilbert $C^*$-modules nuclearity Morita equivalence

Citation

Amini, Massoud; Asadi, Mohammad B. On nuclearity of the algebra of adjointable operators. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 423--427. doi:10.36045/bbms/1442364589. https://projecteuclid.org/euclid.bbms/1442364589


Export citation